Find all the zeros for each polynomial : f(x)=x^7+x^6-x^5-x^4-x^3-x^2+x+1

Question

possible zeros:

total zeros:

synthetic division:

solving a quadratic (if necessary)

answer (list the zeros and the factoted form of f(x) 

Answer 1

By the Rational Root Theorem, all rational roots are in the form p/q, such that p is a factor of the constant and q is a factor of the leading coefficient. The only p/q's are ±1.

 

Using synthetic substitution, neither is a zero.